Question

Determinar a matriz X tal que ½ (X + A) = 3(X +
(B – A)) – C, sendo A, B e C as seguintes matrizes :

A=$\left[\begin{array}{ccc}2&1&0\\1&1&1\end{array}\right]$
B=$\left[\begin{array}{ccc}0&0&2\\6&4&2\end{array}\right]$
C=$\left[\begin{array}{ccc}3&2&0\\0&1&0\end{array}\right]$

Answer 1

Simplificando a equação, teremos: $x= \frac{6.(B-A)-C-A}{-5}$

$6(B-A)=$$\left[\begin{array}{ccc}-12&-6&12\\30&18&6\end{array}\right]$
$C-A=$$\left[\begin{array}{ccc}1&1&1\\-1&0&-1\end{array}\right]$
$6(B-A)-C-A=$$\left[\begin{array}{ccc}-17&-9&12\\29&16&5\end{array}\right]$
$X=$$\left[\begin{array}{ccc}\frac{17}{5}&\frac{9}{5}&-\frac{12}{4}\\&&& \frac{29}{5}& \frac{16}{5}&-1\end{array}\right]$